f(x) = lnx + ∫(1→e) f(x) dx - f'(1)f'(x) = 1/x ==> f'(1) = 1f(x) = lnx + A - 1,A = ∫(1→e) f(x) dxA = ∫(1→e) lnx dx + (A - 1)∫(1→e) dxA = [xlnx - x] |(1→e) + (A - 1)(e - 1)A = (e - e) - (0 - 1...